| Title:
|
Natural homomorphisms of Witt rings of orders in algebraic number fields. II
(English)
|
| Author:
|
Ciemała, Marzena |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| ISSN:
|
1214-8148 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
13-16 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that there are infinitely many real quadratic number fields $K$ with the property that for infinitely many orders $\mathcal {O}$ in $K$ and for the maximal order $R$ in $K$ the natural homomorphism $\varphi :W\mathcal {O}\rightarrow WR$ of Witt rings is surjective. |
| Keyword:
|
Witt ring |
| Keyword:
|
orders in number fields |
| Keyword:
|
bilinear forms on ideals |
| MSC:
|
11E81 |
| MSC:
|
19G12 |
| idZBL:
|
Zbl 1127.11320 |
| idMR:
|
MR2298907 |
| . |
| Date available:
|
2009-12-29T09:18:33Z |
| Last updated:
|
2010-06-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137477 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/131463 |
| . |
| Reference:
|
[1] Ciemała, M.: Natural homomorphisms of Witt rings of orders in algebraic number fields . Math. Slovaca 54 (2004), 473–477. MR 2114618 |
| Reference:
|
[2] Ciemała, M., Szymiczek, K.: On natural homomorphisms of Witt rings . Proc. Amer. Math. Soc. 133 (2005), 2519–2523. MR 2146193 |
| Reference:
|
[3] Ciemała, M., Szymiczek, K.: On injectivity of natural homomorphisms of Witt rings (submitted) . |
| Reference:
|
[4] Czogała, A.: Generators of the Witt groups of algebraic integers . Ann. Math. Siles. 12 (1998), 105–121. MR 1673080 |
| Reference:
|
[5] Milnor, J., Husemoller, D.: Symmetric bilinear forms . Springer-Verlag, Berlin - Heidelberg - New York 1973. Zbl 0292.10016, MR 0506372 |
| Reference:
|
[6] Neukirch, J.: Algebraic number theory . Springer-Verlag, Berlin 1999. Zbl 0956.11021, MR 1697859 |
| Reference:
|
[7] Sierpiński, W.: Teoria Liczb . Monografie Matematyczne, Warszawa 1950. MR 0047060 |
| Reference:
|
[8] Ward, M.: Prime divisors of second order recurring sequences . Duke Math. J. 21 (1954), 607–614). Zbl 0058.03701, MR 0064073 |
| . |